In addition, the Martian atmosphere contains CO2, whose dissociation products are known to include strong radiators. An inviscid, equilibrium , stagnation point, radiation -coupled flow-field code has been developed for investigating blunt-body atmospheric entry. The method has been compared with ground-based and flight data for air, and reasonable agreement has been found. In the present work, the method was applied to a matrix of conditions in the Martian atmosphere. These conditions encompass most trajectories of interest for Mars exploration spacecraft.

The predicted equilibrium radiative heating to the stagnation point of the vehicle is presented. The equilibrium -diffusion limit for radiation hydrodynamics. The equilibrium -diffusion approximation EDA is used to describe certain radiation -hydrodynamic RH environments. When this is done the RH equations reduce to a simplified set of equations.

The EDA can be derived by asymptotically analyzing the full set of RH equations in the equilibrium -diffusion limit. Here, we derive the EDA this way and show that it and the associated set of simplified equations are both first-order accurate with transport corrections occurring at second order. Of course, the radiation pressures are not equivalent. It is expected that simplified physical models and numerical discretizations of the RH equations that do not preserve this first-order accuracy will not retain the correct equilibrium -diffusion solutions.

As a practical example, we show that nonequilibrium-diffusion radiative -shock solutions devolve to equilibrium -diffusion solutions when the asymptotic parameter is small. Incorporation of the equilibrium temperature approach in a Soil and Water Assessment Tool hydroclimatological stream temperature model.

Stream temperature is an important indicator for biodiversity and sustainability in aquatic ecosystems. The stream temperature model currently in the Soil and Water Assessment Tool SWAT only considers the impact of air temperature on stream temperature , while the hydroclimatological stream temperature model developed within the SWAT model considers hydrology and the impact of air temperature in simulating the water-air heat transfer process. In this study, we modified the hydroclimatological model by including the equilibrium temperature approach to model heat transfer processes at the water-air interface, which reflects the influences of air temperature , solar radiation , wind speed and streamflow conditions on the heat transfer process.

The thermal capacity of the streamflow is modeled by the variation of the stream water depth. An advantage of this equilibrium temperature model is the simple parameterization, with only two parameters added to model the heat transfer processes. The model is calibrated and validated at five stations throughout different parts of the ARB, where close to monthly samplings of stream temperatures are available. The results indicate that the equilibrium temperature model proposed in this study provided better and more consistent performances for the different regions of the ARB with the values of the Nash-Sutcliffe Efficiency coefficient NSE greater than those of the original SWAT model and the hydroclimatological model.

To test the model performance for different hydrological and environmental conditions, the equilibrium temperature model was also applied to the North Fork Tolt River Watershed in Washington, United States. The results indicate a reasonable simulation of stream temperature using the model proposed in this study, with minimum relative error values compared to the other two models.

Changes in freshwater ecosystems due to a climate change have been great concern for sustainable river basin management both for water resources utilization and ecological conservation. However, their impact seems to be difficult to evaluate because of wide variety of basin characteristics along a river network both in nature and social environment.

This presentation uses equilibrium water temperature as a simple criterion index for evaluating the long-term changes of stream thermal environment due to the historical climate change in Japan. It examines, at first, the relationship between the equilibrium water temperature and the stream temperature observed for 7 years at a lower reach in the Ibo River, Japan.

It analyzes, then, the seasonal and regional trends of the equilibrium water temperature change for the last 50 years at meteorological station sites throughout Japan, discussing their rising or falling characteristics. The correlation analysis at the local reach of the Ibo River shows that the equilibrium water temperature has similar trend of change as the stream temperature. However, its value tends to be higher than the stream temperature in summer, while lower in winter.

The onset of the higher equilibrium water temperature fluctuates annually from mid February to early April. This onset fluctuation at each spring could be influenced by the different amount of snow at the antecedent winter. The rising or falling trends of the equilibrium water temperature are analyzed both annually and seasonally through the regression analysis of the sites in Japan.

Consequently, the trends of the temperature change could be categorized by 12 patterns. As for the seasonal analysis, the results shows that there are many sites indicating the falling trend in spring and summer, and rising trends in autumn and winter. In particular, winter has the strong rising tendency throughout Japan. As for the regional analysis, the result illustrates the precise rationality; e.

Temperature , ordering, and equilibrium with time-dependent confining forces. PubMed Central. The concepts of temperature and equilibrium are not well defined in systems of particles with time-varying external forces. An example is a radio frequency ion trap, with the ions laser cooled into an ordered solid, characteristic of sub-mK temperatures , whereas the kinetic energies associated with the fast coherent motion in the trap are up to 7 orders of magnitude higher.

Simulations with 1, ions reach equilibrium between the degrees of freedom when only aperiodic displacements secular motion are considered. The coupling of the periodic driven motion associated with the confinement to the nonperiodic random motion of the ions is very small at low temperatures and increases quadratically with temperature.

The advantage of a flowing plasma reactor is that continuous chemical processes can be driven with the flexibility of startup times in the seconds timescale. Here the reduction of CO2 to CO is used as a model system: the complementary diagnostics illustrate how a baseline thermodynamic equilibrium conversion can be exceeded by the intrinsic non- equilibrium from high vibrational excitation. Laser Rayleigh scattering is used to measure the reactor temperature and Fourier Transform Infrared Spectroscopy FTIR to characterize in situ internal vibrational excitation as well as the effluent composition to monitor conversion and selectivity.

Equilibrium temperature in a clump of bacteria heated in fluid. A theoretical model was developed and used to estimate quantitatively the "worst case", i. For clumps with 10 to 10 6 cells heated in vapor, such as dry and moist air, and liquid fluids such as purees and juices, predictions show that temperature equilibrium will occur with sterilization temperatures up to degrees C in under 0.

Model development highlighted that the controlling influence on time for heating up the clump is the surface convection thermal resistance and that the internal conduction resistance of the clump mass is negligible by comparison. The time for a clump to reach equilibrium sterilization temperature was therefore decreased with relative turbulence velocity of the heating fluid, such as occurs in many process operations. These results confirm widely held suppositions that the heat-up time of bacteria in vapor or liquid is not significant with usual sterilization times. Radiative interactions in molecular gases under local and nonlocal thermodynamic equilibrium conditions.

Basic formulations, analyses, and numerical procedures are presented to investigate radiative heat interactions in diatomic and polyatomic gases under local and nonlocal thermodynamic equilibrium conditions. Essential governing equations are presented for both gray and nongray gases. Information is provided on absorption models, relaxation times, and transfer equations.

Radiative flux equations are developed which are applicable under local and nonlocal thermodynamic equilibrium conditions. The problem is solved for fully developed laminar incompressible flows between two parallel plates under the boundary condition of a uniform surface heat flux. For specific applications, three diatomic and three polyatomic gases are considered. The results are obtained numerically by employing the method of variation of parameters.

The results are compared under local and nonlocal thermodynamic equilibrium conditions at different temperature and pressure conditions. Both gray and nongray studies are conducted extensively for all molecular gases considered. The temperature and pressure range considered are K and 0. In general, results demonstrate that the gray gas approximation overestimates the effect of radiative interaction for all conditions.

The conditions of NLTE, however, result in underestimation of radiative interactions. The method developed for this study can be extended to solve complex problems of radiative heat transfer involving nonequilibrium phenomena. The experiments were aimed at measuring the spatially and spectrally resolved radiance at relevant entry conditions for both an approximate Earth atmosphere 79 N2 : 21 O2 as well as a more accurate composition featuring the trace species Ar and CO2 The experiments were configured to target a wide range of conditions, of which shots from 8 to The non- equilibrium component was chosen to be the focus of this study as it can account for a significant percentage of the emitted radiation for Earth entry, and more importantly, non- equilibrium has traditionally been assigned a large uncertainty for vehicle design.

The main goals of this study are to present the shock tube data in the form of a non- equilibrium metric, evaluate the level of agreement between the experiment and simulations, identify key discrepancies and to promote discussion about various aspects of modeling non- equilibrium radiating flows.

Radiance profiles integrated over discreet wavelength regions, ranging from the VUV through to the NIR, were compared in order to maximize both the spectral coverage and the number of experiments that could be used in the analysis. A previously defined non- equilibrium metric has been used to allow comparisons with several shots and reveal trends in the data.

For Earth re-entry at velocities between 8 and The non- equilibrium component was chosen to be the focus of this study as it can account for a significant percentage of the emitted radiation for Earth re-entry, and more importantly, non- equilibrium has traditionally been assigned a large uncertainty for vehicle design. The main goals of this study are to present the shock tube data in the form of a non- equilibrium metric, evaluate the level of agreement between the experiment and simulations, identify key discrepancies and to examine critical aspects of modeling non- equilibrium radiating flows.

Radiance pro les integrated over discreet wavelength regions, ranging from the Vacuum Ultra Violet VUV through to the Near Infra-Red NIR , were compared in order to maximize both the spectral coverage and the number of experiments that could be used in the analysis. Non- equilibrium effects in high temperature chemical reactions. Reaction rate data were collected for chemical reactions occurring at high temperatures during reentry of space vehicles. The principle of detailed balancing is used in modeling kinetics of chemical reactions at high temperatures.

Although this principle does not hold for certain transient or incubation times in the initial phase of the reaction, it does seem to be valid for the rates of internal energy transitions that occur within molecules and atoms. That is, for every rate of transition within the internal energy states of atoms or molecules, there is an inverse rate that is related through an equilibrium expression involving the energy difference of the transition.

We studied waste form strategies for advanced fuel cycle schemes.

## Metals far from equilibrium: From shocks to radiation damage

Several options were considered for three waste streams with the following fission products: cesium and strontium, transition metals, and lanthanides. These three waste streams may be combined or disposed separately. The decay of several isotopes will generate heat that must be accommodated by the waste form, and this heat will affect the waste loadings.

To help make an informed decision on the best option, we present computational data on the equilibrium temperature of glass waste forms containing a combination of these three streams.

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Role of radiative -convective feedbacks in tropical cyclogenesis in rotating radiative -convective equilibrium simulations. Self-aggregation has primarily been studied in a non-rotating framework, but it has been hypothesized to be important to tropical cyclogenesis. In numerical simulations of tropical cyclones, a broad vortex or saturated column is often used to initialize the circulation. Here, we instead allow a circulation to develop spontaneously from a homogeneous environment in 3-d cloud-resolving simulations of radiative -convective equilibrium in a rotating framework, with interactive radiation and surface fluxes and fixed sea surface temperature.

The goals of this study are two-fold: to study tropical cyclogenesis in an unperturbed environment free from the influence of a prescribed initial vortex or external disturbances, and to compare cyclogenesis to non-rotating self-aggregation. We quantify the feedbacks leading to tropical cyclogenesis using a variance budget equation for the vertically integrated frozen moist static energy. In the initial development of a broad circulation, the feedback processes are similar to the initial phase of non-rotating aggregation.

Sensitivity tests in which the degree of interactive radiation is modified are also performed to determine the extent to which the radiative feedbacks that are essential to non-rotating self-aggregation are important for tropical cyclogenesis. Finally, we examine the evolution of the rotational and divergent flow, to determine the point at which rotation becomes important and the cyclogenesis process begins to differ from non-rotating aggregation. Local thermodynamic equilibrium in a laser-induced plasma evidenced by blackbody radiation.

We show that the plasma produced by laser ablation of solid materials in specific conditions has an emission spectrum that is characterized by the saturation of the most intense spectral lines at the blackbody radiance. The blackbody temperature equals the excitation temperature of atoms and ions, proving directly and unambiguously a plasma in local thermodynamic equilibrium.

## Effects of nuclear explosions

The present investigations take benefit from the very rich and intense emission spectrum generated by ablation of a nickel-chromium-molybdenum alloy. This alternative and direct proof of the plasma equilibrium state re-opens the perspectives of quantitative material analyses via calibration-free laser-induced breakdown spectroscopy.

Moreover, the unique properties of this laser-produced plasma promote its use as radiation standard for intensity calibration of spectroscopic instruments. Emergent constraint on equilibrium climate sensitivity from global temperature variability. Equilibrium climate sensitivity ECS remains one of the most important unknowns in climate change science. ECS is defined as the global mean warming that would occur if the atmospheric carbon dioxide CO 2 concentration were instantly doubled and the climate were then brought to equilibrium with that new level of CO 2. Despite its rather idealized definition, ECS has continuing relevance for international climate change agreements, which are often framed in terms of stabilization of global warming relative to the pre-industrial climate.

The possibility of a value of ECS towards the upper end of this range reduces the feasibility of avoiding 2 degrees Celsius of global warming, as required by the Paris Agreement. Here we present a new emergent constraint on ECS that yields a central estimate of 2. Our approach is to focus on the variability of temperature about long-term historical warming, rather than on the warming trend itself. We use an ensemble of climate models to define an emergent relationship between ECS and a theoretically informed metric of global temperature variability.

This metric of variability can also be calculated from observational records of global warming, which enables tighter constraints to be placed on ECS, reducing the probability of ECS being less than 1. ECS is defined as the global mean warming that would occur if the atmospheric carbon dioxide CO2 concentration were instantly doubled and the climate were then brought to equilibrium with that new level of CO2.

### Section 5.0 Effects of Nuclear Explosions

Control of the longitudinal magnetization in fast gradient echo sequences is an important factor enabling the high efficiency of balanced Steady State Free Precession bSSFP sequences. The method is characterized in gradient echo phantom imaging at 3T as a function of feedback gain, phase, and duration and compared with results from numerical simulations of the Bloch equations incorporating RD. Appropriate applications might include improving navigated sequences. Equilibrium structure of solar magnetic flux tubes: Energy transport with multistream radiative transfer.

We examine the equilibrium structure of vertical intense magnetic flux tubes on the Sun. Assuming cylindrical geometry, we solve the magnetohydrostatic equations in the thin flux-tube approximation, allowing for energy transport by radiation and convection. The radiative transfer equation is solved in the six-stream approximation, assuming gray opacity and local thermodynamic equilibrium.

This constitutes a significant improvement over a previous study, in which the transfer was solved using the multidimensional generalization of the Eddington approximation. Convection in the flux tube is treated using mixing-length theory, with an additional parameter alpha, characterizing the suppression of convective energy transport in the tube by the strong magnetic field. The equations are solved using the method of partial linearization. We present results for tubes with different values of the magnetic field strength and radius at a fixed depth in the atmosphere.

In general, we find that, at equal geometric heights, the temperature on the tube axis, compared to the ambient medium, is higher in the photosphere and lower in the convection zone, with the difference becoming larger for thicker tubes. At equal optical depths the tubes are generally hotter than their surroundings. The results are comparatively insensitive to alpha but depend upon whether radiative and convective energy transport operate simultaneously or in separate layers.

A comparison of our results with semiempirical models shows that the temperature and intensity contrast are in broad agreement. However, the field strengths of the flux-tube models are somewhat lower than the values inferred from observations. Asymptotic analysis of discrete schemes for non- equilibrium radiation diffusion.

Motivated by providing well-behaved fully discrete schemes in practice, this paper extends the asymptotic analysis on time integration methods for non- equilibrium radiation diffusion in [2] to space discretizations. Therein studies were carried out on a two- temperature model with Larsen's flux-limited diffusion operator, both the implicitly balanced IB and linearly implicit LI methods were shown asymptotic-preserving.

In this paper, we focus on asymptotic analysis for space discrete schemes in dimensions one and two. Then by employing formal asymptotic analysis, the first-order asymptotic-preserving property for these schemes and furthermore for the fully discrete schemes is shown. Finally, with the help of manufactured solutions, numerical tests are performed, which demonstrate quantitatively the fully discrete schemes with IB time evolution indeed have the accuracy and asymptotic convergence as theory predicts, hence are well qualified for both non- equilibrium and equilibrium radiation diffusion.

A new one-dimensional radiative equilibrium model for investigating atmospheric radiation entropy flux. A new one-dimensional radiative equilibrium model is built to analytically evaluate the vertical profile of the Earth's atmospheric radiation entropy flux under the assumption that atmospheric longwave radiation emission behaves as a greybody and shortwave radiation as a diluted blackbody. Results show that both the atmospheric shortwave and net longwave radiation entropy fluxes increase with altitude, and the latter is about one order in magnitude greater than the former.

The vertical profile of the atmospheric net radiation entropy flux follows approximately that of the atmospheric net longwave radiation entropy flux. Sensitivity study further reveals that a 'darker' atmosphere with a larger overall atmospheric longwave optical depth exhibits a smaller net radiation entropy flux at all altitudes, suggesting an intrinsic connection between the atmospheric net radiation entropy flux and the overall atmospheric longwave optical depth.

These results indicate that the overall strength of the atmospheric irreversible processes at all altitudes as determined by the corresponding atmospheric net entropy flux is closely related to the amount of greenhouse gases in the atmosphere. Temperature lapse rates at restricted thermodynamic equilibrium. Part II: Saturated air and further discussions. In the first part of this work equilibrium temperature profiles in fluid columns with ideal gas or ideal liquid were obtained by numerically minimizing the column energy at constant entropy, equivalent to maximizing column entropy at constant energy.

A minimum in internal plus potential energy for an isothermal temperature profile was obtained in line with Gibbs' classical equilibrium criterion. However, a minimum in internal energy alone for adiabatic temperature profiles was also obtained. This led to a hypothesis that the adiabatic lapse rate corresponds to a restricted equilibrium state, a type of state in fact discussed already by Gibbs. In this paper similar numerical results for a fluid column with saturated air suggest that also the saturated adiabatic lapse rate corresponds to a restricted equilibrium state.

The proposed hypothesis is further discussed and amended based on the previous and the present numerical results and a theoretical analysis based on Gibbs' equilibrium theory. The effects of massive graviton on the equilibrium between the black hole and radiation gas in an isolated box. It is well known that the black hole can have temperature and radiate the particles with black body spectrum, i. Hawking radiation. Therefore, if the black hole is surrounded by an isolated box, there is a thermal equilibrium between the black hole and radiation gas.

A simple case considering the thermal equilibrium between the Schwarzschild black hole and radiation gas in an isolated box has been well investigated previously in detail, i. In this paper, following the above spirit, the effects of massive graviton on the thermal equilibrium will be investigated. For the gravity with massive graviton, we will use the de Rham-Gabadadze-Tolley dRGT massive gravity which has been proven to be ghost free. Because the graviton mass depends on two parameters in the dRGT massive gravity, here we just investigate two simple cases related to the two parameters, respectively.

Our results show that in the first case the massive graviton can suppress or increase the condensation of black hole in the radiation gas although the T-E diagram is similar as the Schwarzschild black hole case. For the second case, a new T-E diagram has been obtained. Moreover, an interesting and important prediction is that the condensation of black hole just increases from the zero radius of horizon in this case, which is very different from the Schwarzschild black hole case.

Ionization equilibrium and radiative energy loss rates for C, N, and O ions in low-density plasmas. The results of calculations of the ionization equilibrium and radiative energy loss rates for C, N and O ions in low-density plasmas are presented for electron temperatures in the range 10,,, K. The ionization structure is determined by using the steady-state corona model, in which electron impact ionization from the ground states is balanced by direct radiative and dielectronic recombination.

With an improved theory, detailed calculations are carried out for the dielectronic recombination rates in which account is taken of all radiative and autoionization processes involving a single-electron electric-dipole transition of the recombining ion. The radiative energy loss processes considered are electron-impact excitation of resonance line emission, direct radiative recombination, dielectronic recombination, and electron-ion bremsstrahlung.

For all three elements, resonance line emission resulting from 2s-2p transitions produces a broad maximum in the energy loss rate near , K. Transport coefficients and heat fluxes in non- equilibrium high- temperature flows with electronic excitation. The influence of electronic excitation on transport processes in non- equilibrium high- temperature ionized mixture flows is studied. Using the modified Chapman-Enskog method, the transport coefficients thermal conductivity, shear viscosity and bulk viscosity, diffusion and thermal diffusion are calculated in the temperature range K.

Thermal conductivity and bulk viscosity coefficients are strongly affected by electronic states, especially for neutral atomic species. Shear viscosity, diffusion, and thermal diffusion coefficients are not sensible to electronic excitation if the size of excited states is assumed to be constant. The limits of applicability for the Stokes relation are discussed; at high temperatures , this relation is violated not only for molecular species but also for electronically excited atomic gases.

Two test cases of strongly non- equilibrium flows behind plane shock waves corresponding to the spacecraft re-entry Hermes and Fire II are simulated numerically. Fluid-dynamic variables and heat fluxes are evaluated in gases with electronic excitation. In inviscid flows without chemical- radiative coupling, the flow-field is weakly affected by electronic states; however, in viscous flows, their influence can be more important, in particular, on the convective heat flux. The contribution of different dissipative processes to the heat transfer is evaluated as well as the effect of reaction rate coefficients.

The competition of diffusion and heat conduction processes reduces the overall effect of electronic excitation on the convective heating, especially for the Fire II test case. It is shown that reliable models of chemical reaction rates are of great. In a humid region like Japan, it seems that the radiation term in the energy balance equation plays a more important role for evapotranspiration then does the vapor pressure difference between the surface and lower atmospheric boundary layer. A Priestley-Taylor type equation equilibrium evaporation model is used to estimate evapotranspiration.

Net radiation , soil heat flux, and surface temperature data are obtained. Only temperature data obtained by remotely sensed techniques are used. Experimental testing of olivine-melt equilibrium models at high temperatures. The most adequate is the model by Ford et al. These data point to the need for developing a new, improved quantitative model of the olivine-melt equilibrium for high- temperature magnesian melts, as well as to the possibility of these studies on the basis of the equipment presented. Non- equilibrium thermionic electron emission for metals at high temperatures.

Stationary thermionic electron emission currents from heated metals are compared against an analytical expression derived using a non- equilibrium quantum kappa energy distribution for the electrons. The calculations accurately predict the measured thermionic emission currents for both high and moderate temperature ranges.

## Chapter 4 — Global Warming of ºC

The Richardson-Dushman law governs electron emission for large values of kappa or equivalently, moderate metal temperatures. The high energy tail in the electron energy distribution function that develops at higher temperatures or lower kappa values increases the emission currents well over the predictions of the classical expression. This also permits the quantitative estimation of the departure of the metal electrons from the equilibrium Fermi-Dirac statistics.

Ionization and thermal equilibrium models for O star winds based on time-independent radiation -driven wind theory. Ab initio ionization and thermal equilibrium models are calculated for the winds of O stars using the results of steady state radiation -driven wind theory to determine the input parameters. Self-consistent methods are used for the roles of H, He, and the most abundant heavy elements in both the statistical and the thermal equilibrium.

The model grid was chosen to encompass all O spectral subtypes and the full range of luminosity classes. Results of earlier modeling of O star winds by Klein and Castor are reproduced and used to motivate improvements in the treatment of the hydrogen equilibrium. The wind temperature profile is revealed to be sensitive to gross changes in the heavy element abundances, but insensitive to other factors considered such as the mass-loss rate and velocity law. The reduced wind temperatures obtained in observing the luminosity dependence of the Si IV lambda wind absorption profile are shown to eliminate any prospect of explaining the observed O VI lambda line profiles in terms of time-independent radiation -driven wind theory.

Temperature in and out of equilibrium : A review of concepts, tools and attempts. We review the general aspects of the concept of temperature in equilibrium and non- equilibrium statistical mechanics. Although temperature is an old and well-established notion, it still presents controversial facets. After a short historical survey of the key role of temperature in thermodynamics and statistical mechanics, we tackle a series of issues which have been recently reconsidered. In particular, we discuss different definitions and their relevance for energy fluctuations.

The interest in such a topic has been triggered by the recent observation of negative temperatures in condensed matter experiments. Moreover, the ability to manipulate systems at the micro and nano-scale urges to understand and clarify some aspects related to the statistical properties of small systems as the issue of temperature 's ;fluctuations;. We also discuss the notion of temperature in a dynamical context, within the theory of linear response for Hamiltonian systems at equilibrium and stochastic models with detailed balance, and the generalized fluctuation-response relations, which provide a hint for an extension of the definition of temperature in far-from- equilibrium systems.

To conclude we consider non-Hamiltonian systems, such as granular materials, turbulence and active matter, where a general theoretical framework is still lacking. How well do simulated last glacial maximum tropical temperatures constrain equilibrium climate sensitivity?

### On the dynamics of hot air plasmas related to lightning discharges: 1. Gas dynamics

This implies that reconstructed LGM cooling in this region could provide information about the climate system ECS value. A radiative forcing and feedback analysis shows that a number of factors are responsible for this decoupling, some of which are related to vegetation and aerosol feedbacks. While several of the processes identified are LGM specific and do not impact on elevated CO2 simulations, this analysis demonstrates one area where the newer CMIP5 models behave in a qualitatively different manner compared with the older ensemble.

The results imply that so-called Earth System components such as vegetation and aerosols can have a significant impact on the climate response in LGM simulations, and this should be taken into account in future analyses. On the time needed to reach an equilibrium structure of the radiation belts. In this paper, we complement the notion of equilibrium states of the radiation belts with a discussion on the dynamics and time needed to reach equilibrium. We find that the equilibrium states at moderately low Kp, when plotted vs L-shell L and energy E , display the same interesting S-shape for the inner edge of the outer belt as recently observed by the Van Allen Probes.

Physically, this shape, intimately linked with the slot structure, is due to the dependence of electron loss rate originating from wave-particle interactions on both energy and L-shell. The time it takes for the flux at a specific L, E to reach the value associated with the equilibrium state, starting from these different initial states, is governed by the initial state of the belts, the property of the dynamics diffusion coefficients , and the size of the domain of computation. Its structure shows a rather complex scissor form in the L, E plane. The equilibrium value phase space density or flux is practically reachable only for selected regions in L, E and geomagnetic activity.

Knowledge about the transformation temperatures is crucial in processing of steels especially in thermomechanical processes because microstructures and mechanical properties after processing are closely related to the extent and type of transformations. The experimental determination of critical temperatures is costly, and therefore, it is preferred to predict them by mathematical methods.

In the current work, new thermodynamically based models were developed for computing the Ae3 and Acm temperatures in the equilibrium cooling conditions when austenite is deformed at elevated temperatures. Academic, New York, pp — Google Scholar. Brenner D Relationship between the embedded-atom method and Tersoff potentials. Brenner DW Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films. Bringa EM Molecular dynamics simulations of Coulomb explosion. Bringa EM, Johnson RE, Papaleo RM Crater formation by single ions in the electronic stopping regime: comparison of molecular dynamics simulations and experiments on organic films.

Cleri F, Rosato V Tight-binding potentials for transition metals and alloys. Definitions, analyses and results. Appl Phys Lett Phys Rev B R. Phys Rev B Google Scholar. Duffy DM, Rutherford AM Including the effects of electronic stopping and electron-ion interactions in radiation damage simulations. Philos Mag A 50 1 See also Erratum, ibid. University of California, Berkeley Google Scholar. Phys Rev B 33 12 Atomic-scale modeling.

Phys Rev B 62 4 — Google Scholar.

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Itoh N, Stoneham A Excitonic model of track registration of energetic heavy ions in insulators. J Phys: Condens Matter Ivanov DS, Zhigilei LV Combined atomistic-continuum modeling of short pulse laser melting and disintegration of metal films. Koponen I Atomic mixing in ion-bombardment-induced temperature spikes in metals.

Figure 4. The size of the Al alloy phase is the pore size of the Ti2AlC foams before infiltration. To that end, two possible mechanisms could explain the formation of TiAl3 and are provided in the Supplementary Information section. Mechanical Properties under Compression. The section below points out that the customized structures could be utilized to tailor mechanical properties and that the rapid infiltration can result in superior mechanical properties of the composites in comparison with their pure constituents.

Both the strength and failure strain of the composites decrease with the size of the Al alloy phase. The differences in the compressive strengths and failure strains lie in the differences in porosity and phase boundary area that are responsible for arresting crack propagations, each of which is illustrated or explained below.

Phase boundary area is responsible for arresting crack propagations see Supplementary Information , and the difference in the phase boundary area relates to the differences in the compressive strength and failure strain. Given a fixed volume percent of interpenetrating phase, the phase boundary area increases with decreasing size of the Al alloy phase.

With the largest phase boundary area, the composite with the finest size of the Al alloy phase has the most effective crack arresting and deflection capabilities and thus exhibits the highest compressive strength and failure strain. Figure 5. At room temperature, the Al alloy in the composite should have mechanical properties comparable with SHT Al alloy due to the rapid high-temperature processing. Figure 5b shows that the specific strength, i.

The importance of the later cannot be overemphasized, especially for applications in which lightweight materials that can carry large loads, such as aerospace and transportation, are essential. Although the strength of the composites is higher than that of PA Al alloy at both room and elevated temperatures, the failure strain of the composites is smaller than that of PA Al alloy.

In other words, the ceramic phase strengthens Al alloy at the expense of its ductility. Thermal Stability. The backscattered SEM images of the composites before and after the heat treatment suggest little growth of the reaction phase and no evidence of interface de-bonding or cracks at the micrometer scale,. Figure 6. The blue, dash line in the plot indicates the yield strength of peak-age Al alloy.

The difference of the compressive strength before and after the heat treatment could come from several changes. First, the heat treatment could relax the residual stresses introduced during the rapid cooling, leading to different initial stress states between as-processed and heat treated composites for both metallic and ceramic phases upon loading.

Second, the heat treatment could change the small misorientation within Al alloy grains. Third, the heat treatment could dissolve precipitates if any in the Al alloy. The last two possible changes would lower the strength of Al alloy in comparison with the Al alloy in the as-processed composites.

The major findings are summarized as follows. The results suggest that the rapid infiltration offers an efficient route for producing interpenetrating ceramic-metal composites with customizable structures by controlling the structure of the ceramic preform. This method can result in composites with superior properties in comparison with those of its constituents. Note that powder mixtures with other volume ratios were also processed to yield Ti2AlC foams with a variety of porosity ranging from vol. Further investigations could be carried out to elaborate the effects of porosity and pore size of the ceramic foams on the infiltration process and properties of the resulting composites.

Pore size of the foams was determined by measuring the size of approximately 50 pores in SEM images using the line intercept method, as specified in ASTM E Four SEM images from randomly selected locations on each sample were used to measure the pore size. Al alloy discs McMaster-Carr, GA with a diameter of 20 mm and a thickness of 4 mm were used for the infiltration process. Composite Sample Preparation.

The "sandwich" set-up enables more uniform infiltration of molten metal. The chamber was evacuated and held at torr for 10 minutes before heating. Graphite foils were applied between samples and graphite die before infiltration. The temperature was calibrated and measured using procedures described elsewhere8. The density and porosity both open and closed were determined by alcohol immersion method based on Archimedes' principle, as specified in ASTM C The theoretical density values of 4. It was assumed that the effect of new phases formed by chemical reactions on the theoretical density is negligible.

The relative density equals the measured value divided by the ROM value, i. The volume of the Al alloy is the measured porosity values of Ti2AlC foams, assuming all pores were filled with Al alloy. The residual porosity of the composites was measured but was not taken into account for the volume ratio approximation. The accelerating voltage and emission current were 15 kV and 20 mA, respectively.

The duration of spot scan of EDS was 60 seconds per spectrum. Further composition measurements were carried out using a Cameca SX electron microprobe with a wavelength dispersive spectrometry WDS system. All samples were cut by electrical discharge machining to dimensions of 3. Barsoum, M. Zhang, Y. Innovations 3, , doi: Peng, L. Fabrication and properties of Ti3AlC2 particulates reinforced copper composites. Scripta Mater. Zhang, Z. Gupta, S. On the tribology of the MAX phases and their composites during dry sliding: A review. Wear , , doi: Wang, W. A , , doi: Hu, L. Alloys Comp.